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Unformatted text preview: O O (1) (1) (7) (7) (9) (9) (6) (6) O O (8) (8) O O O O O O O O O O (2) (2) O O O O O O (5) (5) O O (4) (4) (3) (3) Math 2860U  Assignment 1 September 28, 2010 It's always useful to have a restart at the beginning of your maple session. restart; Problem 1: (supposed to be done by hand , but done in Maple here for fun, so you can see how to use Maple to solve problems stepbystep. Explanations on how you would do this by hand are provided.) Solve the separable ode: ode1 := diff(y(x),x)=8*x^2/(y+3); ode1 := d d x y x = 8 x 2 y C 3 with the initial conditions: x0 := 5; x0 := 5 y0 := 9; y0 := K 9 This equation is both separable and exact. Let's solve as separable. Separate the y to the left side, and the x to the right side, then integrate both sides accordingly. ls := integrate(y+3,y); ls := 1 2 y 2 C 3 y rs := integrate(8*x^2,x); rs := 8 3 x 3 Then the general solution is (don't forget that constant!) gensol:=ls=rs+C; gensol := 1 2 y 2 C 3 y = 8 3 x 3 C C Now to find C, we sub in the initial conditions...by hand, you replace x with 5 and y with 9 and solve for C. subs(x=x0,y=y0,gensol); 27 2 = 1000 3 C C and solve for C solve( (7) ,C); K 1919 6 ok, if doing this by hand, you'd get the solution below. exactsol := subs(C= (8) ,gensol); exactsol := 1 2 y 2 C 3 y = 8 3 x 3 K 1919 6 Since the solution is quadratic in y, there seem to be 2 possible solutions (10) (10) O O O O (14) (14) O O (12) (12) O O O O O O O O (13) (13) O O (18) (18) O O O O (15) (15) O O O O (19) (19) O O (11) (11) O O (17) (17) O O (16) (16) O O sols:={solve(exactsol,y)};...
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 Spring '10
 Kidnan
 Numerical Analysis, initial conditions, Euler, exact solution, =y + h*slope

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